We investigate charge and thermoelectric transport in monolayer graphene containing a dilute distribution of finite-range non-Hermitian scattering centers. The impurities are modeled as circular complex potentials, whose imaginary component describes local carrier loss or gain. By solving the Dirac scattering problem exactly within a partial-wave approach, we obtain the nonunitary scattering matrix and derive the transport and absorption cross sections, which separately characterize momentum relaxation and net carrier exchange with the environment. To connect the microscopic scattering problem with stationary transport, we formulate a semiclassical Boltzmann description in which an external reservoir compensates the equilibrium particle loss or gain. This leads to an effective relaxation time governed by both elastic momentum scattering and non-Hermitian flux exchange. Using the full energy-dependent relaxation time, we evaluate the Onsager coefficients and the resulting electrical conductivity, electronic thermal conductivity, Seebeck coefficient, Lorenz ratio, and electronic thermoelectric figure of merit. We find that weak gain increases the effective carrier lifetime and enhances both charge and heat conductivities, while absorption produces the opposite behavior. More importantly, gain enhances the magnitude of the thermopower and the electronic figure of merit, whereas loss suppresses them. The Lorenz ratio remains close to the Sommerfeld value, with non-Hermiticity mainly modifying its finite-temperature corrections. Our results show that non-Hermitian scattering provides an additional mechanism for controlling the energy dependence of carrier relaxation and, consequently, the thermoelectric response of graphene.